When it comes to the Braves' Hall of Fame era, don't even attempt roll call unless you have some time on your hands.

Yes, there was only one World Series title. Even Bobby Cox, Tom Glavine and Greg Maddux would stipulate to that. But the volume of excellence, and the constantly changing cast of characters behind that excellence, is staggering.

How about six primary shortstops? Seven primary players at each of three other positions -- first base, left field and right field? Twelve closers who had at least 10 saves in a season? Eighteen pitchers that registered double-figure wins in a season?

To produce 1,431 regular-season victories over 15 seasons, winning 14 consecutive division titles (and getting a mulligan for the strike-ended 1994 season), the Braves played in two stadiums, two divisions (they moved from the National League West to the NL East in '94) and used a total of 263 players. Amazingly, there were only 21 starting pitchers, that total reduced by the 25 times that Maddux, Glavine and John Smoltz made 30-plus starts in a season.

"A lot of changes went on during those years," said Cox, the manager who will join Maddux and Glavine in being inducted into the Hall of Fame on Sunday. "But with [general manager] John Schuerholz at the controls, we lost somebody, we got somebody right back."

And no matter who lined up alongside the cornerstone players, a group that included guys like David Justice and Terry Pendleton in the early '90s and later on Chipper Jones and Andruw Jones, the baseball season in Atlanta was certain to extend into October.

Hall of Fame coverage begins at noon ET on Sunday with MLB Tonight live from Cooperstown on MLB Network and simulcast on MLB.com and the At Bat app, with the induction ceremony beginning at 1:30 p.m.

Only once, when Glavine and Mark Wohlers combined on a one-hitter in Game 6 of the 1995 World Series against the Indians, did the Braves win the last game of the season. But the postseason heartbreak that became an annual event shouldn't be used to diminish the greatness of what the Braves did with Schuerholz and Cox in charge.

"I know everybody likes to see the bottom line -- how many World Series did you win? -- but getting into position to be in a World Series is not easy," Joe Torre said. "For them to compete every single year, change personnel every single year and still be there, I always admired that. I always looked at the Braves as an organization that was up there to be respected based on the fact they knew how to do it."

Glavine and his scores of teammates from those years would love at least a couple more World Series rings. It still stings that they let the 1996 Series get away after winning the first two games at Yankee Stadium, and Smoltz and Glavine will never forget the quiet of the visiting clubhouse in Minnesota after Jack Morris outpitched Smoltz in the classic Game 7 in '91.

But more than anything, they're grateful for the long ride they had with a perennial contender.

"I would argue that it's tougher to win 14 straight division titles than it is win two World Series in a given time," Glavine said. "That was always kind of the argument that a lot of us had. During that course of time, the Blue Jays won back-to-back World Series and then they were gone; the Marlins have won a couple World Series, and look at everything that's happened in between. I think from a players' standpoint, given a choice -- would you rather win a couple World Series and endure all those other bad years or would you rather have one World Series and 14 division titles? -- I think a lot of guys would say, 'Give me the 14 division titles and a chance to have a World Series every year.'"

Torre agreed.

"In today's baseball, where you have to go through layers upon layers of playoffs, for them to continuously contend was something to admire," he said. "I still admire that. You look at them, they change personnel every year, but there always seems to be a plan. They stay the plan, which isn't easy. They're quite an organization."

Cox said he worried about complacency but that he never had to push his players too hard. They were as focused on keeping the legacy alive as he was.

"I wanted them to walk like champions, no doubt about that," Cox said. "But on the other hand, I wanted them to remember how they got there. That was with hard work and dedication, and having a little fun in between, too. We had the type of players that were winners. They knew the competition was going to get better each year, and they lived up to what I thought they could actually do."

As great of a feeling as it was to beat the Indians and win a World Series, the one year that compared was 1991.

Cox had started the 1990 season as the Braves' general manager, then he moved into the dugout to replace Russ Nixon after a 25-50 start. The team would go on to lose 97 games, with Cox filling both roles, but in October, team president Stan Kasten imported Schuerholz to be the GM.

There were limited expectations for the 1991 season, but the Braves got better and better as the season went on. They caught the Dodgers in late August and battled them throughout September. Those teams entered the last weekend of the season tied, but Steve Avery and Smoltz beat the Astros on Friday and Saturday, clinching the NL West title with help from the Giants.

The Braves were underdogs against Jim Leyland's Pirates in the NL Championship Series, but Avery and Smoltz came through again in Games 6 and 7 at Three Rivers Stadium, bringing the World Series to Atlanta for the first time.

"The city of Atlanta became a baseball town again," Cox said. "The energy, the excitement, the packed crowds at old Fulton County Stadium, the people honking their horns when you were driving to the ballpark, that type of thing. [There] was so much energy in the city."

It was baseball at its best.

"In many ways, the '91 season was a little more magical than the '95 season, with the whole worst-to-first thing, playing in the World Series, all that being unexpected," Glavine said. "It really caught the city by storm. The excitement level was unlike anything any of us had ever seen and probably have seen since then. That certainly was the one year that was comparable to the '95 season. Then the overall run of success. That's something that we're all very proud of, that we were able to have that run."

Phil Rogers is a columnist for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.